An efficient method for computing the quantum theory of atoms in molecules (QTAIM) topology of the electron density (or other scalar field) is presented. A modified Newton–Raphson algorithm was implemented for finding the critical points (CP) of the electron density. Bond paths were constructed with the second-order Runge–Kutta method. Vectorization of the present algorithm makes it to scale linearly with the system size. The parallel efficiency decreases with the number of processors (from 70% to 50%) with an average of 54%. The accuracy and performance of the method are demonstrated by computing the QTAIM topology of the electron density of a series of representative molecules. Our results show that our algorithm might allow to apply QTAIM analysis to large systems (carbon nanotubes, polymers, fullerenes) considered unreachable until now. © 2012 Wiley Periodicals, Inc.